Related papers: Split-Quaternionic Hopf Map, Quantum Hall Effect, …
By separating the Schr\"odinger equation for $N$ noninteracting spin-polarized fermions in two-dimensional hyperspherical coordinates, we demonstrate that fractional quantum Hall (FQH) states emerge naturally from degeneracy patterns of the…
We exhibit a Hopf superalgebra structure of the algebra of field operators of quantum field theory (QFT) with the normal product. Based on this we construct the operator product and the time-ordered product as a twist deformation in the…
We construct a model of spin-Hall effect on a noncommutative 4 sphere with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum orthogonal group. The corresponding representation theory allows…
The properties of Hopf star operations and twisted Hopf stars operations on quantum groups are discussed in relation with the theory of representations (star representations). Invariant Hermitian sesquilinear forms (scalar products) on…
We investigate theoretically the fractional quantum Hall effect at half-filling in the lowest Landau level observed in asymmetric wide quantum wells. The asymmetry can be achieved by a potential bias applied between the two sides of the…
It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the…
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of…
The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical…
We present a theoretical framework to describe the integer quantum Hall effect (IQHE) in three-dimensional (3D) electron systems. This extends our previous single-electron approach, which was successfully applied to two-dimensional (2D)…
The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are…
We study the many-body ground states of three-component quantum particles in two prototypical topological lattice models under strong intercomponent and intracomponent repulsions. At band filling $\nu=3/4$ for hardcore bosons, we…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy…
We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground…
The fractional quantum Hall effect has been considered as a puzzling quantum many-body phenomenon that has yet to be fully explained. The plateau width and excitation energy gap are particularly problematic. We report here that those two…
We consider an effective model for graphene with interface-induced spin-orbit coupling and calculate the quantum Hall effect in the low-energy limit. We perform a systematic analysis of the contribution of the different terms of the…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
The construction by Zhang and Hu of a four-dimensional analogue of the Quantum Hall effect is generalized and recast as a purely geometrical theory, using the languages of Lie group theory and twistor theory. It emerges that the Zhang-Hu…